Lane-Emden equations perturbed by nonhomogeneous potential in the super critical case

Autor: César E. Torres Ledesma, Ying Wang, Yong Ma
Rok vydání: 2021
Předmět:
Zdroj: CONCYTEC-Institucional
Consejo Nacional de Ciencia Tecnología e Innovación Tecnológica
instacron:CONCYTEC
Advances in Nonlinear Analysis, Vol 11, Iss 1, Pp 128-140 (2021)
ISSN: 2191-950X
2191-9496
2020-0129
DOI: 10.1515/anona-2020-0129
Popis: Our purpose of this paper is to study positive solutions of Lane-Emden equation − Δ u = V u p i n R N ∖ { 0 } $$\begin{array}{} -{\it\Delta} u = V u^p\quad {\rm in}\quad \mathbb{R}^N\setminus\{0\} \end{array}$$ (0.1) perturbed by a non-homogeneous potential V when p ∈ [ p c , N + 2 N − 2 ) , $\begin{array}{} p\in [p_c, \frac{N+2}{N-2}), \end{array}$ where pc is the Joseph-Ludgren exponent. When p ∈ ( N N − 2 , p c ) , $\begin{array}{} p\in (\frac{N}{N-2}, p_c), \end{array}$ the fast decaying solution could be approached by super and sub solutions, which are constructed by the stability of the k-fast decaying solution wk of −Δ u = up in ℝ N ∖ {0} by authors in [9]. While the fast decaying solution wk is unstable for p ∈ ( p c , N + 2 N − 2 ) , $\begin{array}{} p\in (p_c, \frac{N+2}{N-2}), \end{array}$ so these fast decaying solutions seem not able to disturbed like (0.1) by non-homogeneous potential V. A surprising observation that there exists a bounded sub solution of (0.1) from the extremal solution of − Δ u = u N + 2 N − 2 $\begin{array}{} -{\it\Delta} u = u^{\frac{N+2}{N-2}} \end{array}$ in ℝ N and then a sequence of fast decaying solutions and slow decaying solutions could be derived under appropriated restrictions for V.
Databáze: OpenAIRE
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